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- Chaos_game abstract "In mathematics, the term chaos game originally referred to a method of creating a fractal, using a polygon and an initial point selected at random inside it. The fractal is created by iteratively creating a sequence of points, starting with the initial random point, in which each point in the sequence is a given fraction of the distance between the previous point and one of the vertices of the polygon; the vertex is chosen at random in each iteration. Repeating this iterative process a large number of times, selecting the vertex at random on each iteration, and throwing out the first few points in the sequence, will often (but not always) produce a fractal shape. Using a regular triangle and the factor 1/2 will result in the Sierpinski triangle, while creating the proper arrangement with four points and a factor 1/2 will create a display of a \"Sierpinski Tetrahedron\", the three-dimensional analogue of the Sierpinski triangle. As the number of points is increased to a number N, the arrangement forms a corresponding (N-1)-dimensional Sierpinski Simplex.The term has been generalized to refer to a method of generating the attractor, or the fixed point, of any iterated function system (IFS). Starting with any point x0, successive iterations are formed as xk+1 = fr(xk), where fr is a member of the given IFS randomly selected for each iteration. The iterations converge to the fixed point of the IFS. Whenever x0 belongs to the attractor of the IFS, all iterations xk stay inside the attractor and, with probability 1, form a dense set in the latter.The \"chaos game\" method plots points in random order all over the attractor. This is in contrast to other methods of drawing fractals, which test each pixel on the screen to see whether it belongs to the fractal. The general shape of a fractal can be plotted quickly with the \"chaos game\" method, but it may be difficult to plot some areas of the fractal in detail.The \"chaos game\" method is mentioned in Tom Stoppard's 1993 play Arcadia.With the aid of the \"chaos game\" a new fractal can be made and while making the new fractal some parameters can be obtained. These parameters are useful for applications of fractal theory such as classification and identification. The new fractal is self-similar to the original in some important features such as fractal dimension.".
- Chaos_game thumbnail Sierpinski_chaos_animated.gif?width=300.
- Chaos_game wikiPageExternalLink barnsley.mybluemix.net.
- Chaos_game wikiPageExternalLink graftale.html.
- Chaos_game wikiPageID "2572603".
- Chaos_game wikiPageLength "3839".
- Chaos_game wikiPageOutDegree "17".
- Chaos_game wikiPageRevisionID "687141915".
- Chaos_game wikiPageWikiLink Arcadia_(play).
- Chaos_game wikiPageWikiLink Attractor.
- Chaos_game wikiPageWikiLink Category:Chaos_theory.
- Chaos_game wikiPageWikiLink Category:Fractals.
- Chaos_game wikiPageWikiLink Chaos_theory.
- Chaos_game wikiPageWikiLink Dense_set.
- Chaos_game wikiPageWikiLink Fixed_point_(mathematics).
- Chaos_game wikiPageWikiLink Fractal.
- Chaos_game wikiPageWikiLink Fraction_(mathematics).
- Chaos_game wikiPageWikiLink Iterated_function_system.
- Chaos_game wikiPageWikiLink Mathematics.
- Chaos_game wikiPageWikiLink Polygon.
- Chaos_game wikiPageWikiLink Sierpinski_triangle.
- Chaos_game wikiPageWikiLink Simplex.
- Chaos_game wikiPageWikiLink Tom_Stoppard.
- Chaos_game wikiPageWikiLink File:Chaosgame.gif.
- Chaos_game wikiPageWikiLink File:Sierpinski_chaos_animated.gif.
- Chaos_game wikiPageWikiLinkText "Chaos Game".
- Chaos_game wikiPageWikiLinkText "Chaos game".
- Chaos_game wikiPageWikiLinkText "chaos game".
- Chaos_game wikiPageUsesTemplate Template:Reflist.
- Chaos_game subject Category:Chaos_theory.
- Chaos_game subject Category:Fractals.
- Chaos_game type Diacritic.
- Chaos_game type Function.
- Chaos_game type Physic.
- Chaos_game type Redirect.
- Chaos_game comment "In mathematics, the term chaos game originally referred to a method of creating a fractal, using a polygon and an initial point selected at random inside it. The fractal is created by iteratively creating a sequence of points, starting with the initial random point, in which each point in the sequence is a given fraction of the distance between the previous point and one of the vertices of the polygon; the vertex is chosen at random in each iteration.".
- Chaos_game label "Chaos game".
- Chaos_game sameAs Q3129337.
- Chaos_game sameAs Jeu_du_chaos.
- Chaos_game sameAs Քաոսի_խաղ.
- Chaos_game sameAs カオスゲーム.
- Chaos_game sameAs Gra_w_chaos.
- Chaos_game sameAs m.07nx3b.
- Chaos_game sameAs Игра_збрке.
- Chaos_game sameAs Q3129337.
- Chaos_game wasDerivedFrom Chaos_game?oldid=687141915.
- Chaos_game depiction Sierpinski_chaos_animated.gif.
- Chaos_game isPrimaryTopicOf Chaos_game.